Solve the following pair of linear equations by substitution method:

x + y = a—b

ax —by = a² + b²

Given equations are

x + y = a – b …(i)

ax – by = a² + b² …(ii)

From eqⁿ (i), x = a – b – y …(iii)

On substituting x = a – b – y in eqⁿ (ii), we get

⇒ a(a – b – y) – by = a² + b²

⇒ a² – ab – ay – by = a² + b²

⇒ – ab – y(a + b) = b²

⇒ – y(a + b) = b² + ab

Now, on putting y = – b in eqⁿ (iii), we get

⇒ x = a – b – ( – b)

⇒ x = a

Thus, x = a and y = – b is the required solution.